{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>2.4 Numpy与Tensor</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.4.1  torch概述"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "tensor([4, 6])\ntensor([1, 2])\ntensor([4, 6])\n"
    }
   ],
   "source": [
    "\n",
    "import torch\n",
    "\n",
    "x=torch.tensor([1,2])\n",
    "y=torch.tensor([3,4])\n",
    "z=x.add(y)\n",
    "print(z)\n",
    "print(x)\n",
    "x.add_(y)\n",
    "print(x)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.4.2 创建tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([1., 2., 3., 4., 5., 6.])"
     },
     "metadata": {},
     "execution_count": 2
    }
   ],
   "source": [
    "import torch\n",
    "\n",
    "#根据list数据生成tensor\n",
    "torch.Tensor([1,2,3,4,5,6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[0., 0., 0.],\n        [0., 0., 0.]])"
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "source": [
    "#根据指定形状生成tensor\n",
    "torch.Tensor(2,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "tensor([[1., 2., 3.],\n        [4., 5., 6.]])\n"
    }
   ],
   "source": [
    "#根据给定的tensor的形状\n",
    "t=torch.Tensor([[1,2,3],[4,5,6]])\n",
    "print(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "torch.Size([2, 3])"
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "source": [
    "#查看tensor的形状\n",
    "t.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "torch.Size([2, 3])"
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "source": [
    "#shape与size()等价方式\n",
    "t.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[0.0000e+00, 0.0000e+00, 8.4078e-45],\n        [0.0000e+00, 1.4013e-45, 0.0000e+00]])"
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "#根据已有形状创建tensor\n",
    "torch.Tensor(t.size())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "#torch.tensor与torch.Tentor的区别\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#根据一定规则，自动生成tensor的一些例子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[1., 0.],\n        [0., 1.]])"
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "#生成一个单位矩阵\n",
    "torch.eye(2,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[0., 0., 0.],\n        [0., 0., 0.]])"
     },
     "metadata": {},
     "execution_count": 11
    }
   ],
   "source": [
    "#自动生成全是0的矩阵\n",
    "torch.zeros(2,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([ 1.,  4.,  7., 10.])"
     },
     "metadata": {},
     "execution_count": 12
    }
   ],
   "source": [
    "torch.linspace(1,10,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[0.9574, 0.0537, 0.3748],\n        [0.4048, 0.7405, 0.0558]])"
     },
     "metadata": {},
     "execution_count": 13
    }
   ],
   "source": [
    "#生成满足均匀分布随机数\n",
    "torch.rand(2,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[0.2392, 0.3205, 0.2690],\n        [1.1671, 0.4532, 1.8783]])"
     },
     "metadata": {},
     "execution_count": 14
    }
   ],
   "source": [
    "#生成满足标准分布随机数\n",
    "torch.randn(2,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[0., 0., 0.],\n        [0., 0., 0.]])"
     },
     "metadata": {},
     "execution_count": 15
    }
   ],
   "source": [
    "#返回所给数据形状相同，值全为0的张量\n",
    "torch.zeros_like(torch.rand(2,3))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.4.3 修改tensor的形状"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "torch.Size([2, 3])"
     },
     "metadata": {},
     "execution_count": 16
    }
   ],
   "source": [
    "#生成一个形状为2x3的矩阵\n",
    "x = torch.randn(2, 3)\n",
    "#查看矩阵的形状\n",
    "x.size()   #结果为torch.Size([2, 3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "2"
     },
     "metadata": {},
     "execution_count": 17
    }
   ],
   "source": [
    "#查看x的维度\n",
    "x.dim()    #结果为2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[ 0.6142,  0.3997],\n        [-0.9013,  0.4411],\n        [-1.3820,  0.7437]])"
     },
     "metadata": {},
     "execution_count": 18
    }
   ],
   "source": [
    "#把x变为3x2的矩阵\n",
    "x.view(3,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Help on built-in function view:\n\nview(...) method of torch.Tensor instance\n    view(*shape) -> Tensor\n    \n    Returns a new tensor with the same data as the :attr:`self` tensor but of a\n    different :attr:`shape`.\n    \n    The returned tensor shares the same data and must have the same number\n    of elements, but may have a different size. For a tensor to be viewed, the new\n    view size must be compatible with its original size and stride, i.e., each new\n    view dimension must either be a subspace of an original dimension, or only span\n    across original dimensions :math:`d, d+1, \\dots, d+k` that satisfy the following\n    contiguity-like condition that :math:`\\forall i = d, \\dots, d+k-1`,\n    \n    .. math::\n    \n      \\text{stride}[i] = \\text{stride}[i+1] \\times \\text{size}[i+1]\n    \n    Otherwise, it will not be possible to view :attr:`self` tensor as :attr:`shape`\n    without copying it (e.g., via :meth:`contiguous`). When it is unclear whether a\n    :meth:`view` can be performed, it is advisable to use :meth:`reshape`, which\n    returns a view if the shapes are compatible, and copies (equivalent to calling\n    :meth:`contiguous`) otherwise.\n    \n    Args:\n        shape (torch.Size or int...): the desired size\n    \n    Example::\n    \n        >>> x = torch.randn(4, 4)\n        >>> x.size()\n        torch.Size([4, 4])\n        >>> y = x.view(16)\n        >>> y.size()\n        torch.Size([16])\n        >>> z = x.view(-1, 8)  # the size -1 is inferred from other dimensions\n        >>> z.size()\n        torch.Size([2, 8])\n    \n        >>> a = torch.randn(1, 2, 3, 4)\n        >>> a.size()\n        torch.Size([1, 2, 3, 4])\n        >>> b = a.transpose(1, 2)  # Swaps 2nd and 3rd dimension\n        >>> b.size()\n        torch.Size([1, 3, 2, 4])\n        >>> c = a.view(1, 3, 2, 4)  # Does not change tensor layout in memory\n        >>> c.size()\n        torch.Size([1, 3, 2, 4])\n        >>> torch.equal(b, c)\n        False\n\n"
    }
   ],
   "source": [
    "help(x.view)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "tensor([ 0.6142,  0.3997, -0.9013,  0.4411, -1.3820,  0.7437])\n"
    }
   ],
   "source": [
    "#把x展平为1维向量\n",
    "y=x.view(-1)  \n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "torch.Size([6])"
     },
     "metadata": {},
     "execution_count": 21
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "torch.Size([1, 6])"
     },
     "metadata": {},
     "execution_count": 22
    }
   ],
   "source": [
    "#添加一个维度\n",
    "z=torch.unsqueeze(y,0)\n",
    "#查看z的形状\n",
    "z.size()   #结果为torch.Size([1, 6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[ 0.6142,  0.3997, -0.9013,  0.4411, -1.3820,  0.7437]])"
     },
     "metadata": {},
     "execution_count": 23
    }
   ],
   "source": [
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "2"
     },
     "metadata": {},
     "execution_count": 24
    }
   ],
   "source": [
    "a = torch.zeros(4,4)\n",
    "a.dim()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([1., 2., 3., 4.])"
     },
     "metadata": {},
     "execution_count": 25
    }
   ],
   "source": [
    "torch.range(1,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "6"
     },
     "metadata": {},
     "execution_count": 26
    }
   ],
   "source": [
    "#计算Z的元素个数\n",
    "z.numel()   #结果为6\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.4.4 索引操作"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[ 0.3607, -0.2859, -0.3938],\n        [ 0.2429, -1.3833, -2.3134]])"
     },
     "metadata": {},
     "execution_count": 53
    }
   ],
   "source": [
    "#设置一个随机种子\n",
    "torch.manual_seed(100) \n",
    "#生成一个形状为2x3的矩阵\n",
    "x = torch.randn(2, 3)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([ 0.3607, -0.2859, -0.3938])"
     },
     "metadata": {},
     "execution_count": 54
    }
   ],
   "source": [
    "#根据索引获取第1行，所有数据\n",
    "x[0,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([-0.3938, -2.3134])"
     },
     "metadata": {},
     "execution_count": 55
    }
   ],
   "source": [
    "\n",
    "#获取最后一列数据\n",
    "x[:,-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([0.3607, 0.2429])"
     },
     "metadata": {},
     "execution_count": 56
    }
   ],
   "source": [
    "#生成是否大于0的Byter张量\n",
    "mask=x>0\n",
    "#获取大于0的值\n",
    "torch.masked_select(x,mask)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[0, 0],\n        [1, 0]])"
     },
     "metadata": {},
     "execution_count": 57
    }
   ],
   "source": [
    "#获取非0下标,即行，列索引\n",
    "torch.nonzero(mask)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[ 0.3607, -1.3833, -2.3134]])"
     },
     "metadata": {},
     "execution_count": 58
    }
   ],
   "source": [
    "#获取指定索引对应的值,输出根据以下规则得到\n",
    "#out[i][j] = input[index[i][j]][j]  # if dim == 0\n",
    "#out[i][j] = input[i][index[i][j]]  # if dim == 1\n",
    "index=torch.LongTensor([[0,1,1]])\n",
    "torch.gather(x,0,index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[ 0.3607, -0.2859, -0.2859],\n        [-1.3833, -1.3833, -1.3833]])"
     },
     "metadata": {},
     "execution_count": 59
    }
   ],
   "source": [
    "index=torch.LongTensor([[0,1,1],[1,1,1]])\n",
    "a=torch.gather(x,1,index)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[0., 0., 0.],\n        [0., 0., 0.]])"
     },
     "metadata": {},
     "execution_count": 60
    }
   ],
   "source": [
    "#把a的值返回到一个2x3的0矩阵中\n",
    "z=torch.zeros(2,3)\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[ 0.3607, -0.2859,  0.0000],\n        [ 0.0000, -1.3833,  0.0000]])"
     },
     "metadata": {},
     "execution_count": 61
    }
   ],
   "source": [
    "z.scatter_(1,index,a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.4.5 广播机制"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "tensor([[ 0,  1,  2],\n        [10, 11, 12],\n        [20, 21, 22],\n        [30, 31, 32]], dtype=torch.int32)\n"
    }
   ],
   "source": [
    "import torch\n",
    "import numpy as np\n",
    "\n",
    "A = np.arange(0, 40,10).reshape(4, 1)\n",
    "B = np.arange(0, 3)\n",
    "#把ndarray转换为Tensor\n",
    "A1=torch.from_numpy(A)  #形状为4x1\n",
    "B1=torch.from_numpy(B)  #形状为3\n",
    "#Tensor自动实现广播\n",
    "C=A1+B1\n",
    "#我们可以根据广播机制，手工进行配置\n",
    "#根据规则1，B1需要向A1看齐，把B变为（1,3）\n",
    "B2=B1.unsqueeze(0)  #B2的形状为1x3\n",
    "#使用expand函数重复数组，分别的4x3的矩阵\n",
    "A2=A1.expand(4,3)\n",
    "B3=B2.expand(4,3)\n",
    "#然后进行相加,C1与C结果一致\n",
    "C1=A2+B3\n",
    "print(C1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.4.6 遂元操作"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "tensor([[-0.2586, -0.2510,  0.4770]])\ntensor([[1.7414, 1.7490, 2.4770]])\n"
    }
   ],
   "source": [
    "import torch\n",
    "\n",
    "t = torch.randn(1, 3)\n",
    "t1 = torch.randn(3, 1)\n",
    "t2 = torch.randn(1, 3)\n",
    "#t+0.1*(t1/t2)\n",
    "torch.addcdiv(t, 0.1, t1, t2)\n",
    "#计算sigmoid\n",
    "torch.sigmoid(t)\n",
    "#将t限制在[0,1]之间\n",
    "torch.clamp(t,0,1)\n",
    "print(t)\n",
    "#t+2进行就地运算\n",
    "t.add_(2)\n",
    "print(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.4.7 归并操作"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([ 0.,  2.,  4.,  6.,  8., 10.])"
     },
     "metadata": {},
     "execution_count": 64
    }
   ],
   "source": [
    "#生成一个含6个数的向量\n",
    "a=torch.linspace(0,10,6)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[ 0.,  2.,  4.],\n        [ 6.,  8., 10.]])"
     },
     "metadata": {},
     "execution_count": 65
    }
   ],
   "source": [
    "#使用view方法，把a变为2x3矩阵\n",
    "a=a.view((2,3))\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([ 6., 10., 14.])"
     },
     "metadata": {},
     "execution_count": 66
    }
   ],
   "source": [
    "#沿y轴方向累加，即dim=0\n",
    "b=a.sum(dim=0)   #b的形状为[3]\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[ 6., 10., 14.]])"
     },
     "metadata": {},
     "execution_count": 67
    }
   ],
   "source": [
    "#沿y轴方向累加，即dim=0,并保留含1的维度\n",
    "b=a.sum(dim=0,keepdim=True) #b的形状为[1,3]\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.4.8比较操作"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[ 0.,  2.,  4.],\n        [ 6.,  8., 10.]])"
     },
     "metadata": {},
     "execution_count": 68
    }
   ],
   "source": [
    "x=torch.linspace(0,10,6).view(2,3)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor(10.)"
     },
     "metadata": {},
     "execution_count": 69
    }
   ],
   "source": [
    "#求所有元素的最大值\n",
    "torch.max(x)   #结果为10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "torch.return_types.max(\nvalues=tensor([ 6.,  8., 10.]),\nindices=tensor([1, 1, 1]))"
     },
     "metadata": {},
     "execution_count": 72
    }
   ],
   "source": [
    "#求y轴方向的最大值\n",
    "torch.max(x,dim=0)  #结果为[6,8,10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Help on built-in function topk:\n\ntopk(...)\n    topk(input, k, dim=None, largest=True, sorted=True, out=None) -> (Tensor, LongTensor)\n    \n    Returns the :attr:`k` largest elements of the given :attr:`input` tensor along\n    a given dimension.\n    \n    If :attr:`dim` is not given, the last dimension of the `input` is chosen.\n    \n    If :attr:`largest` is ``False`` then the `k` smallest elements are returned.\n    \n    A namedtuple of `(values, indices)` is returned, where the `indices` are the indices\n    of the elements in the original `input` tensor.\n    \n    The boolean option :attr:`sorted` if ``True``, will make sure that the returned\n    `k` elements are themselves sorted\n    \n    Args:\n        input (Tensor): the input tensor.\n        k (int): the k in \"top-k\"\n        dim (int, optional): the dimension to sort along\n        largest (bool, optional): controls whether to return largest or\n               smallest elements\n        sorted (bool, optional): controls whether to return the elements\n               in sorted order\n        out (tuple, optional): the output tuple of (Tensor, LongTensor) that can be\n            optionally given to be used as output buffers\n    \n    Example::\n    \n        >>> x = torch.arange(1., 6.)\n        >>> x\n        tensor([ 1.,  2.,  3.,  4.,  5.])\n        >>> torch.topk(x, 3)\n        torch.return_types.topk(values=tensor([5., 4., 3.]), indices=tensor([4, 3, 2]))\n\n"
    }
   ],
   "source": [
    "help(torch.topk)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "torch.return_types.topk(\nvalues=tensor([[ 6.,  8., 10.]]),\nindices=tensor([[1, 1, 1]]))"
     },
     "metadata": {},
     "execution_count": 73
    }
   ],
   "source": [
    "#求最大的2个元素\n",
    "torch.topk(x,1,dim=0)  #结果为[6,8,10],对应索引为tensor([[1, 1, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([0.1000, 0.6000, 0.3000, 0.9000, 0.4000, 0.7000])"
     },
     "metadata": {},
     "execution_count": 77
    }
   ],
   "source": [
    "a = torch.tensor([0.1,0.6,0.3,0.9,0.4,0.7])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(tensor([0., 0., 0., 0.]), tensor([0, 0, 0, 0]))"
     },
     "metadata": {},
     "execution_count": 92
    }
   ],
   "source": [
    "y = torch.zeros(4),torch.zeros(4,dtype=torch.long)\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(tensor([0.9000, 0.7000, 0.6000, 0.4000]), tensor([3, 5, 1, 4]))"
     },
     "metadata": {},
     "execution_count": 93
    }
   ],
   "source": [
    "torch.topk(a,4,out=y)\n",
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.4.9 矩阵操作"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor(18)"
     },
     "metadata": {},
     "execution_count": 94
    }
   ],
   "source": [
    "a=torch.tensor([2, 3])\n",
    "b=torch.tensor([3, 4])\n",
    "\n",
    "torch.dot(a,b)  #运行结果为18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[ 68, 113,  48,  33],\n        [ 69,  79,  24,  29]])"
     },
     "metadata": {},
     "execution_count": 95
    }
   ],
   "source": [
    "x=torch.randint(10,(2,3))\n",
    "y=torch.randint(6,(3,4))\n",
    "torch.mm(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([[[40, 31, 58, 31],\n         [25, 10, 43, 40]],\n\n        [[28, 28, 32, 32],\n         [57, 23, 42,  8]]])"
     },
     "metadata": {},
     "execution_count": 96
    }
   ],
   "source": [
    "\n",
    "x=torch.randint(10,(2,2,3))\n",
    "y=torch.randint(6,(2,3,4))\n",
    "torch.bmm(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "24"
     },
     "metadata": {},
     "execution_count": 103
    }
   ],
   "source": [
    "y.nelement()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>2.5 Tensor与Autograd</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "2.5.3 标量反向传播"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "x,w,b的require_grad属性分别为：False,True,True\n"
    }
   ],
   "source": [
    "import torch\n",
    "import numpy as np\n",
    "\n",
    "#定义输入张量x\n",
    "x=torch.Tensor([2])\n",
    "#初始化权重参数W,偏移量b、并设置require_grad为True，为自动求导\n",
    "w=torch.randn(1,requires_grad=True)\n",
    "b=torch.randn(1,requires_grad=True)\n",
    "y=torch.mul(w,x)  #等价于w*x\n",
    "z=torch.add(y,b)  #等价于y+b\n",
    "#查看x,w，b页子节点的requite_grad属性\n",
    "print(\"x,w,b的require_grad属性分别为：{},{},{}\".format(x.requires_grad,w.requires_grad,b.requires_grad))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "y，z的requires_grad属性分别为：True,True\nx，w，b，y，z的是否为叶子节点：True,True,True,False,False\nx，w，b的grad_fn属性：None,None,None\ny，z的是否为叶子节点：<MulBackward0 object at 0x000001E85EFA2848>,<AddBackward0 object at 0x000001E85EFA8148>\n"
    }
   ],
   "source": [
    "#查看非叶子节点的requres_grad属性,\n",
    "print(\"y，z的requires_grad属性分别为：{},{}\".format(y.requires_grad,z.requires_grad))\n",
    "#因与w，b有依赖关系，故y，z的requires_grad属性也是：True,True\n",
    "#查看各节点是否为叶子节点\n",
    "print(\"x，w，b，y，z的是否为叶子节点：{},{},{},{},{}\".format(x.is_leaf,w.is_leaf,b.is_leaf,y.is_leaf,z.is_leaf))\n",
    "#x，w，b，y，z的是否为叶子节点：True,True,True,False,False\n",
    "#查看叶子节点的grad_fn属性\n",
    "print(\"x，w，b的grad_fn属性：{},{},{}\".format(x.grad_fn,w.grad_fn,b.grad_fn))\n",
    "#因x，w，b为用户创建的，为通过其他张量计算得到，故x，w，b的grad_fn属性：None,None,None\n",
    "#查看非叶子节点的grad_fn属性\n",
    "print(\"y，z的是否为叶子节点：{},{}\".format(y.grad_fn,z.grad_fn))\n",
    "#y，z的是否为叶子节点：<MulBackward0 object at 0x7f923e85dda0>,<AddBackward0 object at 0x7f923e85d9b0>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "参数w,b的梯度分别为:tensor([2.]),tensor([1.]),None\n非叶子节点y,z的梯度分别为:None,None\n"
    }
   ],
   "source": [
    "#基于z张量进行梯度反向传播,执行backward之后计算图会自动清空，\n",
    "#如果需要多次使用backward，需要修改参数retain_graph为True，此时梯度是累加的\n",
    "#z.backward(retain_graph=True)\n",
    "z.backward()\n",
    "#查看叶子节点的梯度，x是叶子节点但它无需求导，故其梯度为None\n",
    "print(\"参数w,b的梯度分别为:{},{},{}\".format(w.grad,b.grad,x.grad))\n",
    "#参数w,b的梯度分别为:tensor([2.]),tensor([1.]),None\n",
    "\n",
    "#非叶子节点的梯度，执行backward之后，会自动清空\n",
    "print(\"非叶子节点y,z的梯度分别为:{},{}\".format(y.grad,z.grad))\n",
    "#非叶子节点y,z的梯度分别为:None,None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "非叶子节点y,z的梯度分别为:None,None\n"
    }
   ],
   "source": [
    "print(\"非叶子节点y,z的梯度分别为:{},{}\".format(y.grad,z.grad))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.5.4 非标量反向传播"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "output_type": "error",
     "ename": "NameError",
     "evalue": "name 'backward' is not defined",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-37-54d6b8a2c176>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mbackward\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mgradient\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mretain_graph\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcreate_graph\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mFalse\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m: name 'backward' is not defined"
     ]
    }
   ],
   "source": [
    "backward(gradient=None, retain_graph=None, create_graph=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "\n",
    "#定义叶子节点张量x，形状为1x2\n",
    "x= torch.tensor([[2, 3]], dtype=torch.float, requires_grad=True)\n",
    "#初始化Jacobian矩阵\n",
    "J= torch.zeros(2 ,2)\n",
    "#初始化目标张量，形状为1x2\n",
    "y = torch.zeros(1, 2)\n",
    "#定义y与x之间的映射关系：\n",
    "#y1=x1**2+3*x2，y2=x2**2+2*x1\n",
    "y[0, 0] = x[0, 0] ** 2 + 3 * x[0 ,1]\n",
    "y[0, 1] = x[0, 1] ** 2 + 2 * x[0, 0]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#y.backward(torch.Tensor([[1, 1]]))\n",
    "#print(x.grad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "tensor([[4., 3.],\n        [2., 6.]])\n"
    }
   ],
   "source": [
    "#生成y1对x的梯度\n",
    "y.backward(torch.Tensor([[1, 0]]),retain_graph=True)\n",
    "J[0]=x.grad\n",
    "#梯度是累加的，故需要对x的梯度清零\n",
    "x.grad = torch.zeros_like(x.grad)\n",
    "#生成y2对x的梯度\n",
    "y.backward(torch.Tensor([[0, 1]]))\n",
    "J[1]=x.grad\n",
    "#显示jacobian矩阵的值\n",
    "print(J)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<h3>2.6 使用Numpy实现机器学习</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(100) \n",
    "x = np.linspace(-1, 1, 100).reshape(100,1) \n",
    "y = 3*np.power(x, 2) +2+ 0.2*np.random.rand(x.size).reshape(100,1)  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# 画图\n",
    "plt.scatter(x, y)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 随机初始化参数\n",
    "w1 = np.random.rand(1,1)\n",
    "b1 = np.random.rand(1,1) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lr =0.001 # 学习率\n",
    "\n",
    "for i in range(800):\n",
    "    # 前向传播\n",
    "    y_pred = np.power(x,2)*w1 + b1\n",
    "    # 定义损失函数\n",
    "    loss = 0.5 * (y_pred - y) ** 2\n",
    "    loss = loss.sum()\n",
    "    #计算梯度\n",
    "    grad_w=np.sum((y_pred - y)*np.power(x,2))\n",
    "    grad_b=np.sum((y_pred - y))\n",
    "    #使用梯度下降法，使loss最小\n",
    "    w1 -= lr * grad_w\n",
    "    b1 -= lr * grad_b\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "tags": []
   },
   "outputs": [
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[[2.98927619]] [[2.09818307]]\n"
    }
   ],
   "source": [
    "plt.plot(x, y_pred,'r-',label='predict')\n",
    "plt.scatter(x, y,color='blue',marker='o',label='true') # true data\n",
    "plt.xlim(-1,1)\n",
    "plt.ylim(2,6)  \n",
    "plt.legend()\n",
    "plt.show()\n",
    "print(w1,b1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>2.7 使用Tensor及antograd实现机器学习</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import torch as t\n",
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "torch.Size([100])"
     },
     "metadata": {},
     "execution_count": 106
    }
   ],
   "source": [
    "t.manual_seed(100) \n",
    "dtype = t.float\n",
    "a =torch.linspace(-1, 1, 100)\n",
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "torch.Size([100, 1])"
     },
     "metadata": {},
     "execution_count": 107
    }
   ],
   "source": [
    "#生成x坐标数据，x为tenor，形状为100x1\n",
    "x = t.unsqueeze(a, dim=1) \n",
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "torch.Size([100, 1])"
     },
     "metadata": {},
     "execution_count": 108
    }
   ],
   "source": [
    "#生成y坐标数据，y为tenor，形状为100x1，另加上一些噪音\n",
    "y = 3*x.pow(2) +2+ 0.2*torch.rand(x.size())  \n",
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# 画图，把tensor数据转换为numpy数据\n",
    "plt.scatter(x.numpy(), y.numpy())\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 随机初始化参数，参数w，b为需要学习的，故需requires_grad=True\n",
    "w = t.randn(1,1, dtype=dtype,requires_grad=True)\n",
    "b = t.zeros(1,1, dtype=dtype, requires_grad=True) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lr =0.001 # 学习率\n",
    "\n",
    "for ii in range(800):\n",
    "    # forward：计算loss\n",
    "    y_pred = x.pow(2).mm(w) + b\n",
    "    loss = 0.5 * (y_pred - y) ** 2\n",
    "    loss = loss.sum()\n",
    "    \n",
    "    # backward：自动计算梯度\n",
    "    loss.backward()\n",
    "    \n",
    "    # 手动更新参数，需要用torch.no_grad()更新参数\n",
    "    with t.no_grad():\n",
    "        w -= lr * w.grad\n",
    "        b -= lr * b.grad\n",
    "    \n",
    "    # 梯度清零\n",
    "        w.grad.zero_()\n",
    "        b.grad.zero_()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "tags": []
   },
   "outputs": [
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "tensor([[2.9645]], requires_grad=True) tensor([[2.1146]], requires_grad=True)\n"
    }
   ],
   "source": [
    "plt.plot(x.numpy(), y_pred.detach().numpy(),'r-',label='predict')#predict\n",
    "plt.scatter(x.numpy(), y.numpy(),color='blue',marker='o',label='true') # true data\n",
    "plt.xlim(-1,1)\n",
    "plt.ylim(2,6)  \n",
    "plt.legend()\n",
    "plt.show()\n",
    "        \n",
    "print(w, b)\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.7.7 64-bit ('d2l': conda)",
   "language": "python",
   "name": "python37764bitd2lconda94fc7ab78ae34cabbef0e75f5636f253"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}